[Establishing and applying of autoregressive integrated moving average model to predict the incidence rate of dysentery in Shanghai].

Objective: To explore the feasibility of establishing and applying of autoregressive integrated moving average (ARIMA) model to predict the incidence rate of dysentery in Shanghai, so as to provide the theoretical basis for prevention and control of dysentery.

Methods: ARIMA model was established based on the monthly incidence rate of dysentery of Shanghai from 1990 to 2007. The parameters of model were estimated through unconditional least squares method, the structure was determined according to criteria of residual un-correlation and conclusion, and the model goodness-of-fit was determined through Akaike information criterion (AIC) and Schwarz Bayesian criterion (SBC). The constructed optimal model was applied to predict the incidence rate of dysentery of Shanghai in 2008 and evaluate the validity of model through comparing the difference of predicted incidence rate and actual one. The incidence rate of dysentery in 2010 was predicted by ARIMA model based on the incidence rate from January 1990 to June 2009.

Results: The model ARIMA (1, 1, 1) (0, 1, 2)(12) had a good fitness to the incidence rate with both autoregressive coefficient (AR1 = 0.443) during the past time series, moving average coefficient (MA1 = 0.806) and seasonal moving average coefficient (SMA1 = 0.543, SMA2 = 0.321) being statistically significant (P < 0.01). AIC and SBC were 2.878 and 16.131 respectively and predicting error was white noise. The mathematic function was (1-0.443B) (1-B) (1-B(12))Z(t) = (1-0.806B) (1-0.543B(12)) (1-0.321B(2) x 12) micro(t). The predicted incidence rate in 2008 was consistent with the actual one, with the relative error of 6.78%. The predicted incidence rate of dysentery in 2010 based on the incidence rate from January 1990 to June 2009 would be 9.390 per 100 thousand.

Conclusion: ARIMA model can be used to fit the changes of incidence rate of dysentery and to forecast the future incidence rate in Shanghai. It is a predicted model of high precision for short-time forecast.